If ∫ 1 1 - c o t x d x = A x + B l o g s i n x - c o s x + c then A + B = …

Step-by-step solution

Let l = ∫ 1 1 - c o t x d x = ∫ 1 1 - c o s x s i n x d x = ∫ s i n x s i n x - c o s x d x = 1 2 ∫ 2 s i n x s i n x - c o s x d x = 1 2 ∫ s i n x + s i n x + c o s x - c o s x s i n x - c o s x d x = 1 2 ∫ s i n x + c o s x + s i n x - c o s x s i n x - c o s x d x = 1 2 [ ∫ d x + ∫ s i n x + c o s x s i n x - c o s x d x Let s i n x - c o s x = t ⇒ c o s x + s i n x d x = d t ∴ l = 1 2 ∫ d x + ∫ 1 t d t = 1 2 x + log ⁡ t + C = 1 2 x + log ⁡ s i n x - c o s x + C = x 2 + 1 2 log ⁡ s i n x - c o s x + C Here